OCR Thursday 14 October 2021 – Afternoon A Level Further Mathematics A Y542/01 Statistics

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Answer all the questions. 1 At a seaside resort the number X of ice-creams sold and the temperature Y  °F were recorded on 20 randomly chosen summer days. The data can be summarised as follows.... /x = 1506 /x2 = 127542 / y = 1431 / y2 = 104451 /xy = 111 297 (a) Calculate the equation of the least squares regression line of y on x, giving your answer in the form y = a + bx. [3] (b) Explain the significance for the regression line of the quantity /[ ( y a i i - + x b)] 2. [1] (c) It is decided to measure the temperature in degrees Centigrade instead of degrees Fahrenheit. If the same temperature is measured both as f  ° Fahrenheit and c° Centigrade, the relationship between f and c is c = 9 5 ( . f-32) Find the equation of the new regression line. [2] 2 A discrete random variable D has the following probability distribution, where a is a constant. d 0 2 4 6 P(D = d ) a 0.1 0.3 0.2 Determine the value of Var(3D + 4). [7] 3 In a large collection of coloured marbles of identical size, the proportion of green marbles is p. One marble is chosen randomly, its colour is noted, and it is then replaced. This process is repeated until a green marble is chosen. The first green marble chosen is the Xth marble chosen. (a) You are given that p = 0.3. (i) Find P( ) 5 1 G G X 0 . [2] (ii) Determine the smallest value of n for which P(X = n) 1 0.1. [2] (b) You are given instead that Var(X  ) = 42. Determine the value of E(X  ). [5]3 © OCR 2021 Y542/01 Oct21 Turn over 4 A random sample of 160 observations of a random variable X is selected. The sample can be summarised as follows. n = 160 /x = 2688 /x2 = 48398 (a) Calculate unbiased estimates of the following. (i) E(X  ) [1] (ii) Var(X  ) [3] (b) Find a 99% confidence interval for E(X  ), giving the end-points of the interval correct to 4 significant figures. [3] (c) Explain whether it was necessary to use the Central Limit Theorem in answering (i) part (a), [1] (ii) part (b). [1] 5 The numbers of each of 9 items sold in two different supermarkets in a week are given in the following table. Item 1 2 3 4 5 6 7 8 9 Supermarket A 17 28 41 43 62 69 75 93 115 Supermarket B 24 7 18 12 47 29 58 42 37 A researcher wants to test whether there is association between the numbers of these items sold in [Show More]

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